To measure the areal density distribution of cold fuel at the maximum compression time during the stagnation phase of implosion in inertial confinement fusion (ICF), we have established the ps-laser driven high-energy X-ray radiography using source-coded technique. This paper describes the design and employment of the object including character-object and pinhole array. Based on the object, the source distribution and the object radiography was obtained at the same shot and same angle of view, and therefore the source-coded radiography of ps-laser driven X-ray has been established in experiments for the first time. From the experimental work on Xingguang-III facility, the spatial resolution of the inversion image with W wire-array target is 5.4 μm±0.7 μm. The efficiency of converting laser energy to high-energy bremsstrahlung (50-200 keV) is 5.4×10^-4 in W wire-array target and 4.8×10^-4 in Au single-wire target, respectively. It is possible that the the source-coded radiography of ps-laser driven X-ray in this work could account for overcoming the balance between spatial resolution and brightness in traditional X-ray backlight by ps-laser. The source-coded radiography provides an important method for ICF implosion backlight to get high resolution high signal-to-noise ratio images under the strong background.